A386746 a(n) = n^3*sigma_2(n).

0, 1, 40, 270, 1344, 3250, 10800, 17150, 43520, 66339, 130000, 162382, 362880, 373490, 686000, 877500, 1396736, 1424770, 2653560, 2482958, 4368000, 4630500, 6495280, 6448510, 11750400, 10171875, 14939600, 16140060, 23049600, 20535538, 35100000, 28658942, 44728320

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..9000

Formula

G.f.: Sum_{k>=1} k^5*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4. - Amiram Eldar, Aug 01 2025

a(n) = n^3*A001157(n).

Dirichlet g.f.: zeta(s-3)*zeta(s-5). - R. J. Mathar, Aug 03 2025

Sum_{k=0..n} a(k) ~ zeta(3) * n^6 / 6. - Amiram Eldar, Nov 11 2025

Mathematica

Table[n^3*DivisorSigma[2, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[Sum[k^5*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x]

Prog

(Magma) [0] cat [n^3*DivisorSigma(2, n): n in [1..35]]; // Vincenzo Librandi, Aug 02 2025

Crossrefs

Cf. A001157, A002117, A328259, A386745.

Sequence in context: A374240 A247406 A229588 * A334121 A117216 A035099

Adjacent sequences: A386743 A386744 A386745 * A386747 A386748 A386749

Keyword

nonn,mult,easy

Author

Vaclav Kotesovec, Aug 01 2025

Status

approved